A rotating electric resolver is an electromagnetic device which is used to accurately indicate the angular position of the rotor with reference to some fixed frame of reference. A typical embodiment of such a resolver comprises an input winding and a pair of output windings. The output windings are typically identical to each other but are wound with a 90 degree phase displacement relative to each other. Consequently, their electrical outputs are similar except for 90 degree phase displacement in time between them. Therefore, if one of the output windows produces an output signal that is proportional to the sine of the angle that the rotor makes with a reference axis at some instant of time, then the other output winding will produce an output signal that will be proportional to the cosine of the same angle. The following formula represents this event: sin (.theta.+90.degree.)=cos .theta..
If one knows the values for sin .theta. and cos .theta. at any instant, then one can compute the value of .theta., for this value will be unique. Knowing .theta. is equivalent to knowing the rotor position at any predetermined instant of time.
There are two basic types of conventional resolvers. One type has sliprings and brushes. The input winding is located in punched laminations housed in the stator. The output windings are located in laminations mounted on the rotor shaft. The electrical outputs of the output windings are led to the sliprings, and collected by stationary brushes that ride on the rotating sliprings. In the other type of conventional resolver, the input winding is located in the rotor, while the output windings are located in the stator. An additional set of magnetically coupled coils on both the stator and the rotor is used to convey the input voltage to the rotating input by inductive or transformer action in these coils.
As is apparent, any device that has sliding contacts and/or rotating windings is more expensive to manufacture and is inherently less reliable than a device which has only stationary windings.
In an attempt to eliminate the above-mentioned drawbacks of conventional resolvers, alternative designs have been heretofore produced in which the input as well as the output windings are all located in the stator laminations in an electrically insulated configuration from each other. The rotor itself carries no windings and merely consists of slots and teeth that do not conform to any mathematically defined shape. As exemplified in the prior art, the function of the slots and teeth is only to abruptly vary the airgap between pairs of rotor teeth, so that a voltage is generated in the output windings as the rotor teeth whip past them. This is caused by a rapid change of reluctance in accordance with Faraday's Law of Induced Voltages. However, in generating an output signal in this manner, the output wave-form contains a high harmonic content which introduces electrical noise which results in serious inaccuracies. In fact, this type of resolver is only a scaled-down version of the well-known inductor alternator that is used for producing high frequency currents for eddy current steel melting furnaces.
A more sophisticated version of this principle was first disclosed by Kronacher in 1957. In the Kronacher apparatus, the input and output windings are all located in the stator. The rotor has slots that again do not conform to any mathematically defined shape. Waveform improvement was effected by introducing the concept of varying the number of turns in each coil of one output winding according to a cosine formula and varying the number of turns in the coils of the other output winding according to a sine formula. This resulted in all of the output coils being different from each other not only in the number of turns but also in their wire gauge sizes. The manufacture of this device is extremely complicated, whether done by manual or automatic means. Furthermore, the output waveform was not free of harmonics since the rotor slotting was abrupt, as in the earlier prior art devices. Insofar as is known, Kronacher's design did not lead to a commercially viable product. The next development in the area is exemplified by the Ringland U.S. Pat. No. 3,641,467. Ringland attempts to avoid the inherent deficiencies in the Kronacher apparatus by expressing a desire to vary the airgap permeance sinusoidally. As stated in Ringland, "Sinusoidal variation of the permeances . . . will result if rotor 27 is contoured as shown to have sinusoidal variation of airgap spacings to teeth 1-6 . . . " (Column 3, lines 35-39). Unfortunately, this statement is flatly wrong both in theory and in practice. According to electromagnetic theory, the stated objective in Ringland '467 is achieved not by varying the airgap sinusoidally, but by a sinusoidal variation of the reciprocal of the airgap spacing. Therefore, any design made in accordance with the teachings of Ringland '467 functions with a pronounced harmonic content in the output waveform. This was apparently recognized, by inference, in the Ringland Patent, since the crests of the rotor lobes shown in FIGS. 7 and 11 of the '467 Patent have been flattened somewhat in comparison to their shape as defined mathematically and mapped in FIG. 9. The fundamental flaw in the '467 Patent is, in fact, a fatal one and, insofar as is known, devices of the general type described in the '467 Patent have not gained acceptance in the marketplace.